One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,

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:<math> Stokes \, I = \frac{RR^* + LL^*}{2} = XX^* + YY^*</math>

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:<math> Stokes \, V = \frac{RR^* - LL^*}{2} = i(XX^* - YY^*)</math>

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For completeness:

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:<math>

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\begin{align}

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Stokes \, Q = XX^* - YY^*\\

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Stokes \, U = XY^* - YX^*

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\end{align}

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</math>

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:<math> P_{linear} = \sqrt{U^2 + Q^2} </math>

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:<math> \Theta = \frac{1}{2}\tan^{-1}{\frac{U}{Q}} </math>

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When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.

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The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by &pi;/2 for both XY* and YX* according to:

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== Polarization Mixing Correction ==

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Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas